On the variance of single-run unbiased stochastic derivative estimators

Zhenyu Cui, Michael C. Fu, Jian Qiang Hu, Yanchu Liu, Yijie Peng, Lingjiong Zhu

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We analyze the variance of single-run unbiased stochastic derivative estimators. The distribution of a specific conditional expectation characterizes an intrinsic distributional property of the derivative estimators in a given class, which, in turn, separates two of the most popular single-run unbiased derivative estimators, infinitesimal perturbation analysis and the likelihood ratio method, into disjoint classes. In addition, a necessary and sufficient condition for the estimators to achieve the lowest variance in a certain class is provided, as well as insights into finding an estimator with lower variance. We offer a sufficient condition to substantiate the rule of thumb that the infinitesimal perturbation analysis estimator has a smaller variance than does the likelihood ratio method estimator and to provide a counterexample when the sufficient condition is not satisfied.

Original languageEnglish
Pages (from-to)390-407
Number of pages18
JournalINFORMS Journal on Computing
Volume32
Issue number2
DOIs
StatePublished - Mar 2020

Keywords

  • Infinitesimal perturbation analysis
  • Likelihood ratio method
  • Simulation
  • Stochastic derivative estimation
  • Variance

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